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Question 6: In what region of space is the potential due to a uniform closed sphere the same as that of a point charge? In what region it differs from that of a point charge?

ANSWER

According to Coulomb’s law the electric potential due to a point charge at a distance r is,e98c11p12 Now consider the case of a sphere of radius R on which the charge is uniformly distributed. As the charge is spherically symmetric, we apply Gauss’s law. Enclose the sphere in a closed concentric surface of radius of r > R. Since the charge enclosed by the surface is the charge on the given charged sphere, therefore, it acts like a point charge and the potential on the closed surface is same like a point charge, that is,e100c11p12e99c11p12  

So, at any point outside the sphere, the charge distribution acts like a point charge.

On the other hand, if we consider the interior of the charged sphere, that is, r < R, and take a Gaussian closed surface to apply Gauss law, then no charge will be enclosed in the closed surface. Therefore, the net electric intensity inside the charged sphere would be zero.

Since E = -ΔV/Δr ⇒ ΔV/Δr = 0. Or ΔV = 0, that is, potential is constant. Therefore, inside the sphere, the potential is different from that of a point charge.

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